If a cosmic ray proton approaches the Earth from outer space along a line toward the center of the Earth that lies in the plane of the equator, in what direction will it be deflected by the Earth’s magnetic field? What about an electron? A neutron?

The direction of the force on the moving charge is perpendicular to the plane formed by the motion of the particle and the direction of the magnetic field. Therefore the direction of the force due to the magnetic field on a moving charge is given by the right-hand rule (RHR).

Please have a look at the above image for an understanding of the right-hand rule.

For a proton, the magnetic flux lines will point toward the north, the thumb would point towards the middle of the world, then the palm would show the east (right) direction.

For the electron the charge is reverse of the proton, therefore the direction of the attraction will be reversed, and the direction of the attraction on the electron will be in the west (left) direction.

Since the neutron is the uncharged particle, there wouldn't be any force on it in due to the magnetic field, thus it'll not be deflected.